Question

which of the following shows the prime factorization of 90? (a) $3^2 \cdot 10$ (b) $2 \cdot 9 \cdot 5$ (c) $2 \cdot 3^2 \cdot 5$ (d) $2^3 \cdot 3 \cdot 5$

Explanation:

Step1: Factor 90 into small primes

$90 = 9 \times 10$

Step2: Factor 9 and 10 further

$9 = 3^2$, $10 = 2 \times 5$

Step3: Combine all prime factors

$90 = 2 \times 3^2 \times 5$

Step4: Match with options

Check each option:

• a) $3^2 \cdot 10$: 10 is not prime
• b) $2 \cdot 9 \cdot 5$: 9 is not prime
• c) $2 \cdot 3^2 \cdot 5$: All factors are prime
• d) $2^3 \cdot 3 \cdot 5$: $2^3=8$, $8 \times 3 \times 5=120

eq 90$

Answer:

c) $2 \cdot 3^2 \cdot 5$